Thoughts of the Champions League are fading at Everton and, as the howls that greeted Norwich City's late equaliser testified, the loss of momentum is largely self-inflicted. Goodison Park was in unforgiving mood as a defensive lapse allowed Sébastien Bassong to salvage a point for Chris Hughton's improving side.

David Moyes has cited profligacy and injury as reasons for Everton's fine start stumbling to a halt and both were a factor here. His side should have established a comfortable lead following a third goal in three starts from Steven Naismith and lacked the personnel to react to Norwich's second-half transformation. But – and it is a problem that has plagued them all season – their defence no longer acts as an insurance against wasteful displays. Everton appeared to have weathered the visitors' recovery when Tim Howard and John Heitinga stood and watched Bassong head home a Javier Garrido free-kick in the 90th minute.

The Everton manager, who has seen top-four aspirations checked by a run of one win in seven games and faces Arsenal, Manchester City and Tottenham in the next three outings, was in no mood to protect his players afterwards. "I didn't think it was a free-kick but I thought they [Howard and Heitinga] both could have done better," he said. "The ball was in the air long enough for the goalkeeper to come for it.

"It is hard to take. We started well and controlled the game. Norwich grew into it and had a few opportunities, but I thought we had got through that and looked more likely to add a second than concede an equaliser towards the end." Moyes responded to a query on whether he was worried about a top-four finish with a simple: "I am."

Hughton's concerns about the Norwich performance had evaporated by the time Bassong, the former Newcastle and Tottenham defender, had extended his team's unbeaten run to seven matches in all competitions. Norwich arrived with confidence high after last week's defeat of Manchester United and a third consecutive clean sheet, but belief and defensive solidity were absent as Everton dominated the first half. Their point, however, was deserved after a second-half display in which Richard Snodgrass, Grant Holt and Anthony Pilkington, twice, all threatened to equalise before Bassong's goal.

"Over the 90 minutes I thought we deserved it," said the Norwich manager. "We conceded a soft goal by our standards of late and didn't keep the ball well in the first half. Everton were certainly the better team. But at 1-0 down you have to open up and ask more of the players and we got that. A point at Goodison is a very big point."

Injuries caused Moyes to shift Phil Jagielka to right-back for Everton and a one-match suspension for Marouane Fellaini meant Thomas Hitzlsperger and Bryan Oviedo had to seize rare opportunities in midfield. Both delivered, particularly Oviedo on his full Premier League debut following his £1.5m arrival from FC Copenhagen, and combined superbly to give Everton an early lead.

Norwich had not ventured out of their half when Hitzlsperger floated a fine ball down the wing where Oviedo controlled on his chest and slipped easily away from Steven Whittaker. He glanced up and rolled the ball perfectly into the path of Naismith, who sidefooted into the roof of John Ruddy's net.

The Scotland international has begun to find the goalscoring touch that convinced Moyes to capitalise on the chaos at Rangers this summer and sign Naismith as a free agent. He, Leon Osman and Leighton Baines had further chances to extend Everton's lead but a terrible touch from Naismith, clean through and attempting to square for the unmarked Nikica Jelavic, proved costly.

As the game entered its 90th minute, and Moyes sprung from his seat in protest at a free-kick given against Steven Pienaar, Garrido curled the set piece towards the back post. Not for the first time this season Howard was nowhere, Heitinga likewise, and Bassong duly capped Norwich's recovery with a downward header.